# Synthetic long stock

**ADV-15a · Advanced Options · Advanced**

**Lesson question:** How does synthetic long stock express a linear bullish exposure view?

Original fictional examples; educational writing, not live market data, orders or production approval.

## By the end

- Read and reconstruct the priced ticket.
- Reconcile leg P/L with the combined graph.
- Explain the time, volatility and operational failure cases.

**Prerequisites:** OPT-F01, OPT-F02, OPT-F03, OPT-F04

A long call plus a short put at the same strike and expiry produces a linear terminal exposure. The identity behind it is max(S−K,0)−max(K−S,0)=S−K. The two option names reduce to one directional slope at settlement.

## Construction: read every leg

At equal illustrative premiums, entry cash is zero and terminal P/L is 100×(S−100). Same strike and expiry are essential. Real premium differences reflect financing, dividends and implementation, so zero premium is an example rather than a universal quote.

## Read the ticket before the graph

BUY means you own an option right; SELL means you accept a short-option obligation. Positive quantities are long and negative quantities are short in the calculation. Check quantity, call/put, strike, multiplier and expiry before netting premium.

All legs in this example share November 20, 2026 expiration. The entry observation is October 6, 2026, with fictional QLT at 100. These are independent illustrative premiums, not a current option chain or executable quotes. The terminal diagram assumes every leg and any shares are resolved at one common settlement price.

## Before expiry: time and volatility

Matching European call and put Gamma/Vega cancel in BSM. Delta is e^(−qT) per unit, not always exactly one with continuous yield. Exercise, funding, dividends and borrowing can make the practical position differ from shares.

## Manage the position deliberately

Treat it as leveraged ownership with a put obligation. Compare financing and costs with stock or futures. Expiry and any rollover require a plan; they are not automatic continuation of the exposure.

## Priced fictional ticket

Read every leg before interpreting the combined payoff.

| Action | Quantity | Type | Strike | Expiry | Premium per unit | Multiplier |

|---|---:|---|---:|---|---:|---:|

| BUY | 1 | call | 100 | 2026-11-20 | 4.2 | 100 |

| SELL | 1 | put | 100 | 2026-11-20 | 4.2 | 100 |

Opening option cash: 0 USD (positive received, negative paid). Entry option fees: 1.3 USD.

$0.65 per option contract on entry only. No exit, assignment, financing or tax costs modeled.

Independent fictional premiums, not one simultaneous arbitrage-consistent chain. All legs realized simultaneously at intrinsic at the same expiry; terminal calculations do not model American early exercise, temporary unhedged positions, forced liquidation or live liquidity. Displayed chart domain is not a tail-risk cap.

**Before fees:** maximum terminal profit Unbounded in this terminal model; maximum terminal loss magnitude 10,000; breakeven price(s) 100.

**After entry fees:** maximum terminal profit Unbounded in this terminal model; maximum terminal loss magnitude 10,001.3; breakeven price(s) 100.013.

## From opening cash to a settlement result

Read the opening instructions: buy 1 100 call at 4.20; sell 1 100 put at 4.20. Option opening cash is $0.00 received as a credit. A received credit is not earned profit while the obligation remains open.

Set the common settlement price to 90.00. Calls have intrinsic value max(S−K,0); puts have max(K−S,0). Subtract the opening premium from each intrinsic value, then multiply by signed quantity and the 100-unit multiplier. Shares contribute their price change from their own cost. The calculation popup shows every leg.

The combined result is $-1,000.00 before costs and $-1,001.30 after illustrative opening fees of $1.30. Exit fees, slippage, funding, dividends and taxes are not included. Opening fees are 0.65 per option contract, not a statement of any broker's pricing.

Maximum terminal profit is unbounded in this model; maximum terminal loss magnitude is $10,000.00, before costs. Isolated zero-P/L settlement points in the model: 100. Move the scenario slider across each strike and explain why the slope changes there. A strike is a contract threshold, not a prediction.

This terminal model is useful for comparing risk shapes, but actual American-style assignment, share delivery, forced liquidation or a failed multi-leg exit can produce a different path. A long protective leg is not an automatic instruction that a broker must exercise it when another leg is assigned.

## Calculation popup: Calculate this exact ticket

```text
P/L = Σ[q × multiplier × (intrinsic − opening premium)] + shares × (S−share entry) − costs
```

Intrinsic is nonnegative before the signed quantity is applied. This is a fictional terminal calculation.

1. +1 × 100 × (0.00 − 4.20) = $-420.00: 100 call.

2. -1 × 100 × (10.00 − 4.20) = $-580.00: 100 put.

3. Opening fees: 1.30.

**Result:** Before costs $-1,000.00; after entry fees only $-1,001.30.

## Calculation popup: Maximum risk and breakevens

```text
Evaluate S=0, all strikes and the final tail slope; solve P/L=0 on each linear segment.
```

Same-expiry payoffs are piecewise linear. A finite chart range cannot prove a tail is bounded.

1. Maximum terminal profit is unbounded in this model; maximum terminal loss magnitude is $10,000.00, before costs.

2. Breakeven points: 100.

3. Costs shift net P/L downward without moving the strikes.

**Result:** Maximum terminal profit is unbounded in this model; maximum terminal loss magnitude is $10,000.00, before costs.

## Graph: The whole ticket at common expiry

**Horizontal:** Underlying settlement price (USD)  
**Vertical:** P/L per complete ticket (USD)

Solid combined curve is before fees; the second includes only the stated entry fees. Individual-leg lines explain construction. This is terminal intrinsic P/L, not current option value. Price can move outside the displayed range.

Complete numerical data are embedded in `scripts/advanced-options/ADV-15a.js` and displayed as an accessible table in the HTML lesson.

## The failure case

At stock zero, a no-debit entry loses 10,000. The short put removed the long call's limited-loss property.

## Check your understanding

### What is whole-position terminal P/L at QLT 90.00, before costs?

**Answer:** $-1,000.00

**Why:** Use all signed legs, not just the winning leg. The popup and graph use the same ticket.

### Does a terminal loss bound guarantee every early-assignment or liquidation outcome?

**Answer:** No.

**Why:** It describes the specified common-settlement payoff. Product rules, stock delivery, capital and execution still matter. **Critical risk check.**

## Takeaway

Explain the intended linear bullish exposure exposure, each leg's obligation and the adverse price region before using the strategy name.

## References and provenance

The cited references support definitions and conventions. The teaching prose, tickets and numerical scenarios are original; they are not attributed as historical market observations.

- [OIC Strategy Reference](https://www.optionseducation.org/strategies/all-strategies-en)

- [OCC Options Disclosure Document](https://www.theocc.com/company-information/documents-and-archives/options-disclosure-document)